Relativity of Simultaneity and Eternalism: In Defense of the

Block Universe

Daniel Peterson∗and Michael Silberstein†

March 2, 2009

AbstractEver since Hermann Minkowski’s now infamous comments in 1908 concerning the

proper way to view space-time, the debate has raged as to whether or not the universeshould be viewed as a four-dimensional, unified whole wherein the past, present, andfuture are equally real or whether the views espoused by the possibilists, historicists,and presentists regarding the unreality of the future (and, for presentists, the past) aremore accurate. Now, a century after Minkowski’s proposed block universe first sparkeddebate, we present a new, more conclusive argument in favor of the eternalism. Utilizingan argument based on the relativity of simultaneity in the tradition of Putnam andRietdijk and novel but reasonable assumptions as to the nature of “reality”, we showthat the past, present, and future should be treated as equally real, thus ruling thatpresentism and other theories of time that bestow special ontological status to the past,present, or future are untenable. Finally, we will respond to our critics who suggestthat: 1) there is no metaphysical difference between the positions of eternalism andpresentism, 2) the present must be defined as the “here” as well as the “now”, or 3)presentism is correct and our understanding of relativity is incomplete because it doesnot incorporate a preferred frame. We call response 1 deflationary since it purportsto dissolve or deconstruct the age-old debate between the two views and response 2compatibilist because it does nothing to alter special relativity (SR) arguing insteadthat SR unadorned has the resources to save presentism. Response 3 we will callincompatibilism because it adorns SR in some way in order to save presentism a lasome sort of preferred frame. We show that neither 1 nor 2 can save presentism and 3is not well motivated at this juncture except as an ad hoc device to refute eternalism.

1 Introduction

As Ladyman et al.[14] wisely note, the following are distinct, but frequently conflated,deeply related issues in the metaphysics of time:∗Department of Philosophy, University of Michigan, Ann Arbor, MI 48109; petersod@umich.edu†Department of Philosophy, Elizabethtown College, Elizabethtown, PA 17022 and Department of Phi-

losophy, University of Maryland, College Park, MD 20742; silbermd@etown.edu

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(i) Are all events, past, present and future, real?(ii) Is there temporal passage or objective becoming?(iii) Does tensed language have tenseless truth conditions?(iv) Does time have a privileged direction?

This paper will focus almost exclusively on question (i). In the philosophy of time, thismajor conundrum has captivated philosophers for decades now. This problem stems fromtwo competing notions of time. The first, originally suggested by Heraclitus, is called pre-sentism1. Though we will later clarify the presentist position in more definite terms so thatit can be made relevant to a more thorough and modern treatment of presentist/eternalistdebate, a good starting definition for presentism is the view that only the present is real;both the past and the future are unreal2 . This view is close to, but not exactly the sameas, possibilism, which states that the future is unreal while both the past and the presentare real. Both of these stances claim to adequately capture the manifest human perceptionof time. We tend to view ourselves as occupying a unique temporal frame that we call thepresent that always moves away from the past towards an uncertain future.

However, with the advent of relativity, a different stance, whose primary ancient pro-ponent was Parmenides of Elea, provided a viable alternative to Heraclitean presentism.This new stance, eternalism, was translated into the language of relativity of HermannMinkowski in 1908 to suggest that time and space should be united in a single, four-dimensional manifold. Thus arose the notion of a 4D “block universe” (BU) in whichthe past, present, and future are all equally real. This view is called eternalism, and twoarguments by Putnam[18] and Rietdijk[19] allegedly show that SR with its relativity ofsimultaneity (RoS) implies that only the BU perspective can obtain.

This paper proceeds as follows. First, we examine the basic structure of the RoS eter-nalism argument suggested by Putnam, Rietdijk, and more recently Stuckey, Silberstein,and Cifone[29][30][25][26] (hereafter SSC) and present our own novel interpretation or ver-sion of the argument for eternalism. Following our proposal, we suggest various points ofcontention that presentists and possibilists might exploit or have exploited in seeking toeither refute eternalism or collapse the presentism/eternalism dichotomy. We have com-piled a reasonably exhaustive taxonomy of possible outs that the presentist or possibilistcould take to avoid the argument from RoS for BU3 . After elaborating our own version

1Recent defenders of presentism include Bourne[2], Craig[6], and Smith[7], whom we take to be ourprimary presentist opponents for the purposes of this discussion.

2What is meant here by “real” is the topic of great debate (see Dorato (2006) and Savitt (2006) for moreon this issue), and we will later clarify our criteria for reality in such a way that many of the vagaries thatarise from an imprecise definition of “real” are dismissed.

3One possible refutation of the RoS argument, derived from the work of Harvey Brown (Brown 2005,Brown and Pooley 2006), suggests a kind of re-interpretation of Minkowski space-time as a codification ofthe behavior of matter as opposed to representing the geometrical structure of space-time. Our response isto be found in Appendix A but has not been integrated into the paper at large because the objection doesnot fit smoothly into our primary taxonomy.

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of the argument, we respond to each counter-argument and show that these objections donot dismiss RoS’s problems for presentism.

2 The Argument from the Relativity of Simultaneity

2.1 General Outline and Definition of Terms

Before presenting our RoS argument against presentism, we first provide a general outlineof RoS arguments for eternalism and give preliminary definitions of some relevant terms.The general form of the arguments against presentism utilized by Putnam, Rietdijk, andSSC goes as follows:

1. Define presentism2. Define the term “co-real”4

3. Show that the consequences of the definition of “co-real” and RoScontradict presentism4. Conclude that presentism is false from the conjunction of 1 and 35. Conclude that eternalism is true from the rejection of presentism

To begin with, we must provide our own definitions for the terms that form the foundationof our revamped version of the RoS argument. The first term to be defined is “presentism”.Presentism is a kind of realism that takes as real only those events5 which occur in thepresent. For instance, since we are sitting next to our friend Joe who is currently readinga paper, the event of his reading a paper and the event of our writing this paper are bothreal while the event of Joe’s leaving to eat dinner is not real because it has not happenedyet and the event of our leaving to eat lunch is not real because it has already happened. Interms of simultaneity, then, one can define presentism as the view that the only real thingsare those which are simultaneous with a given present event. Eternalism, by contrast, isthe view that all events past, present, and future are equally real. Thus, Joe’s reading,our typing, Joe’s leaving for dinner, and our leaving for lunch are all equally real despite

4The actual term “co-real” appears only in the SSC papers, but since these present the most recentincarnation of the RoS argument against presentism, we follow their terminology here. It should be notedthat Rietdijk does not provide an analysis of reality in his paper, and while Putnam does discuss somebasic assumptions about reality that are necessary for his argument to go through, they are not argued foror supported in any great detail.

5We use the term “events” here to bypass any concerns that may arise due to the identity of individualslike those raised by French and Krause[12] or issues of endurance and perdurance. Such issues as identityand endurance/perdurance, while interesting, need not directly bear on this debate, and so we invoke eventsthat are assumed to be of infinitely small extension and duration (as such they should be fully understoodonly in terms of their identifying coordinates) to bypass such debates. We are not committed to the claimthat such events are in some way the atomistic components of what exists in space-time; rather, we simplyinvoke them to avoid begging the question on issues like identity and endurance/perdurance.

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the fact that one of these events has already occurred while another has yet to occur.Eternalists hold that all events are equally real, regardless of whether or not said eventsare simultaneous.

There are two elements, then, that are important for establishing both presentismand eternalism: reality and simultaneity. The debate presupposes that there is a unique(non-equivocal) sense of the term reality that both sides share. The dispute thereforeis over whether or not present events have some ontologically privileged status qua theirproperty of “existing at time some time t where t is in the present”. To this end we willfirst minimally characterize the terms “reality” and “simultaneity” for use in the contextof our revamped argument. Before beginning, we should emphasize that we are beingpurposefully vague with our first characterization of reality here so as to determine reality’smost general non-equivocal properties which we will build upon later in this paper. Twoevents which “share reality” as we characterize it share a single, unique feature (i.e., thesame ontological status with respect to realness); this uniqueness, we believe, is the absoluteminimal criterion an event would have to satisfy for it to be considered “real” in anymeaningful sense of the word.

To better understand the minimal sense of reality at work here, we define two separateprinciples: the “reality value” and “reality relation.” “Reality values” or “R-values” canbe thought of as representing the ontological status of any given event. Within space-time,every event can be assigned an R-value that denotes its ontological status, and there is aone-to-one and onto mapping of possible R-values onto ontological statuses. In the interestof defining reality generally, we will not attempt to enumerate how many R-values exist,but one could easily take reality to be binary and thus assert that, for any event, if itsR-value is 1, that event “is real”, and if its R-value is 0, that event “is not real.” One coulduse higher values like 2 and higher to denote other states, such as “possibly real”, “realin the future”, etc., but, as previously stated, we will not attempt to enumerate all suchpossible R-values here6. It should be pointed out that our uniqueness criterion on realitytranslates into this system simply as the claim that every event has a single unique R-value.This seems intuitive since an event with an R-value of both 1 and 0, on our scheme, wouldbe both real and unreal, which would be a contradiction.

Our other sense of reality as expressed in the “reality relation” will be essential to ourdiscussion of co-reality. The reality relation can be recast as the idea of “equal reality” andexists between any two or more events that can be considered “equally real.” Translated interms of R-values, a reality relation exists between any two events that must have the sameR-value. For instance, if events A and B are equally real, then the R-value of event A isthe same as the R-value of event B. One should notice here that our definition of “equallyreal” does not assume that two equally real events are both “real”; equally real events Aand B may have whatever R-value you please as long as the R-values are the same for

6See Appendix B for a more nuanced view of R-values and possible objections to the RoS argument thatone might raise based on our naive characterization of R-values described here.

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both A and B. This relation explains what a presentist means when she says, “The presentis the only thing that is real” since the presentist will hold that events in the future andthe past will have different R-values from events in the present7. Thus, our purposefullylimited characterization of the “equally real” relation has been defined so as to be usefulin a definition of co-reality.

As for simultaneity, if it is possible for one to construct a hyperplane of simultaneity(i.e. a four-dimensional manifold in space-time constructed in such a way that all of theevents connected by this manifold must be space-like separated from one another) betweenany two or more events, then these events are said to be simultaneous. Such simultaneousevents are required to be space-like separated events that appear to be simultaneous in somesubluminal inertial reference frame. Light-like and time-like separated events cannot havea hyperplane of simultaneity constructed between them. Also, a hyperplane of simultaneitymay be drawn between any two space-like separated events, meaning that the space-likeseparation of events A and B is necessary and sufficient for their simultaneity.

Combining the criteria of equal reality (“equally real” means that two events havethe same R-value) and simultaneity (“simultaneous” means that two events are space-like separated such that a hyperplane of simultaneity can be constructed between thetwo events) gives us the relation of “co-reality”, which refers to, as the name suggests,two events that are equally real and “simultaneous.” The presentist perspective can berestated in terms of this “co-reality” as the stance that “simultaneity between events isa necessary and sufficient condition for the reality (that is, for both events sharing theR-value 1 corresponding to “real”) of these events if at least one of these events occurs inthe ‘present’ ”. For the presentist, any two space-like separated points are thus co-real aswe have defined “co-reality”. Our restatement of presentism in terms of co-reality here isthe assumption that we alluded to in step 1 above.

7To reiterate, what we have characterized here is the minimal position a presentist must take with regardto a characterization of reality. It might be objected that, at this point, we have not actually defined “whatreality is.” We will cash out a richer notion of reality later in the paper so that we are careful not to begthe question against critics like Savitt and Dorato; for now, we are characterizing reality only to a minimaldegree in an attempt to determine the properties of the “co-reality” relation, and as such we need onlyendorse the minimal sense of reality that bears upon our discussion of co-reality.

The presentist might object to our characterization of her conception of reality, but to refuse the char-acterization of reality we have provided here would be to take an anti-realist stance since a non-uniqueor equivocal conception of reality would make the idea of “reality” a useless concept for the purposes ofthis debate. Thus, the presentist cannot argue against our minimal characterization of reality and remaina committed presentist, and the same goes for the eternalist. In the words of Dolev, if one denies thisminimal ontological assumption then “neither the tensed nor the tenseless view has the final word in themetaphysics of time.”

The presentist could argue against us on the grounds that it is relations, perhaps, that are fundamentallyreal and not events; this, however, would simply lead us to re-atomize our space-time such that theserelations become the fundamental ontic units which assume R-values and the relation of “equally real”connects two such lesser relations. Therefore, even if one makes an argument that forces us to change thefundamental ontic units of our setup, our basic characterization of R-values and “equal reality” can standunadulterated.

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Figure 1: RoS Proof Space-Time Diagram

Our previous examples should make our notion of co-reality more explicit. For instance,the presentist takes Joe’s paper reading and our paper typing are co-real events becausethey are space-like separated, meaning that there exists some frame in which these twoevents are simultaneous. However, our paper typing and our leaving for lunch are time-likeseparated, so there is no sub-luminal frame in which these two events are simultaneousand they are therefore not co-real. These two criteria of reality and simultaneity as wehave defined them are necessary and sufficient for our use of “co-real”, and so we turn nextto our RoS argument that utilizes this notion of “co-reality” to reveal the contradictorynature of presentism when combined with relativity.

2.2 RoS Argument8

Consider the following situation: our friends John and Josephine stub their toes at thesame time in my stationary reference frame9. The event of John stubbing his toe is labeledA in Figure 1 and the event of Josephine stubbing her toe is labeled as B in Figure 1.At a later time (but again, simultaneously in our rest frame), both Josephine and Johnshout in pain from stubbing their respective toes. John’s shout of pain is labeled A′ whileJosephine’s shout of pain is labeled B′ in Figure 1. I note that in my frame, both toe-stubs

8One could argue that, having already defined “co-reality” as we have, the RoS argument has alreadybeen made for us: any two space-like separated points are equally real, and space-likeness is not transitive(i.e. A and B could be space-like separated and B and C space-like separated but A and C time-likeseparated), so we must conclude that any two events (time-like, light-like, or space-like separated from eachother) are equally real. The RoS argument in II.2, however, is a bit more nuanced than the argumentjust proposed, and it makes it easier for one to determine which definitions and assumptions about realityplay what role in the argument. As such, we hope the reader will bear with the exposition for this longerargument.

9We are assuming that these “toe-stubs” in this example are the kind of events described in footnote 5for the reasons stated in that footnote.

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occur at time t1 in Figure 1. Thus, events A and B are simultaneous and co-real as perthe previously-established criteria.

Now, some time before this the alien battle cruisers P and D pass each other directlyover our heads. The primed axes refer to the frame for battle cruiser P and the double-primed axes refer to the frame for battle cruiser D. Both of these battle cruisers tell adifferent story from ours. For battle cruiser P events B and A′ occur at the same time,and thus B and A′ are equally real per co-reality. For battle cruiser D, however, events B′

and A occur at the same time, and thus B‘ and A are equally real per co-reality. We nowintroduce the symbol “r” to stand for “shares an R-value with” or “is equally real with”.The following three statements are true (at least from someone’s perspective):

ArBBrA′

B′rA

From the previously established criteria for equal reality, we can establish two importantfacts about co- real events α, β, and γ. First, if αrβ is true, then βrα is true since R-valuesare unique. Thus, the operator “r” is commutative. This fact must be true since equalreality is an equivalence relation10. The second important fact about equal reality is thatthe co-real operator is transitive, even across frames. That means that if αrβ is the caseand βrγ is the case, then αrγ must also be the case. This follows directly as consequenceof our definition for equal reality11. Thus, applying the properties of transitivity andcommutativity to the above relations, we arrive at the result that:

ArA′

10One might object that, for historicists and possibilists in particular, the “co-real” relation is not anequivalence relation. For instance, right now the Norman Invasion is “real” to us because it is in our past,and so the historicist/possibilist would want to say that such an event is as real as our writing this paper;however, at the time of the Norman Invasion, we were not yet born, so we were “not real” at that time.The equal reality relation only holds one way.

However, one can respond to this claim by citing the fact that the equal reality of simultaneous eventsis an equivalence relation in historicism and possibilism even if the “equal reality” relation in general isnot. Two events that happen at the same time must be equally real if it is temporality alone that bestowsmetaphysical status on events. The above argument only necessitates the treatment of “equal reality”as an equivalence relation for cases where the two “equally real” relata are space-like separated and thussimultaneous. In such a case, equal reality is an equivalence relation even for historicists and possibilists.Thus, the fact that equal reality is not necessarily an equivalence relation in general does not mean thatequal reality is not an equivalence relation in the case of simultaneity; in fact, the opposite is true.

11This feature of co-reality is perhaps not intuitive, but a simple conceptual argument can show whyequal reality, as we have defined it, must be a transitive property. If two events A and B are co-real in agiven frame, this means that they share an R-value. Likewise, co-real events B and C must also share aunique R-value. Since the uniqueness criterion on reality implies that the R-value shared by A and B mustbe the same R-value shared by B and C, it then follows that A and C must have the same R-value as well,and thus they must be equally real.

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BrB′

Generalizing from this result, then, one can conclude that a prior event (the stubbing of atoe) is as real as a later event (a shout of pain). If the first event (A, for instance) occurs inthe “present”, then A′ occurs in the future and the RoS argument suggests that the futureis as real as the present. Likewise, if A′ occurs in the present, then A occurs in the past andthe RoS argument suggests that the past is as real as the present. Both of these conclusionscontradict the presentist assertion that the present is real while the past and future arenot since past, present, and future must share the same ontological status by the aboveargument. Since presentism in conjunction with relativity and our other basic assumptionsleads to a contradiction, presentism must be false given our assumptions. Finally, sincevariations of this argument would answer equally well anyone who would argue that onlythe past is real or only the future is real, the only conclusion left for a realist is thateternalism must be correct since both presentism and possibilism must be discarded. Wehave thus achieved our goal of constructing a rigorous argument for eternalism from RoS inthe tradition of Rietdijk, Putnam, and SSC though our argument provides a more detailedanalysis of the assumptions about the nature of “is real” that go into this kind of argument.

3 Presentist Points of Contention

There are several points in the above argument for eternalism that presentists (or anti-realists, for that matter) could attack or have attacked. The point of this section is toprovide a basic taxonomy of points of contention presentists utilize or could utilize todisagree with both the argument presented above and eternalism in general.

3.1 Deflationary Objections: No Presentist/Eternalist Distinction

The first attack on the RoS argument which works equally well on any argument tryingto prove or disprove eternalism is that there is, in fact, no metaphysical or empiricaldistinction between the views supported by presentists and those supported by eternalists.This collapse of the dichotomy between presentism and eternalism is most ardently arguedfor by Savitt[22] and Dorato[11] in recent papers. Both of these papers utilize semanticarguments to suggest that the distinction between presentism and eternalism boils downto a difference in definitions for “real” which translates, in various contexts, to differencesin tensed versus tenseless existence claims. These two authors claim that presentism andeternalism are both essentially either vacuously true when viewed with the proper definitionof existence (for instance, to say that the present is the only thing that “exists now” istautological since “now” is defined in terms of the present) or analytically false when viewedwith the improper sense of existence (for instance, to say that the present is the only thingthat “exists tenselessly” is to ignore the past and future that are assumed in the phrase“exists tenselessly”). These two authors go on to attack various defenses of eternalism that

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rely on modality and various other semantic considerations, leading them to the conclusionthat the problem posed by the presentist/eternalist debate is truly a non-starter by way ofa “Wittgenstein-like” or “Austin-like” deflation.

In an earlier paper , Dorato[10] brings in various other semantic arguments againsteternalism specifically in an attempt to show how eternalism is as problematic as presen-tism. The first contention Dorato raises is against the eternalist perspective that “thepast, present, and future are all real at the same time”, which he views as meaninglesssince one cannot say anything about the relationship between the past, present, and futureat a given time since all three temporal regions cannot be simultaneous. There must be atemporal separation between the past, present, and future for them to be well defined, soany statement about how the past, present, and future interact at a given time collapsesthis distinction and thus becomes meaningless. The second argument against eternalismon semantic grounds is that an eternal truth like “event A takes place at time t” maybe timeless, but the object of this statement, event A, is not necessarily as timeless asthe statement about it. Dorato thus believes that eternalism confuses the following twostatements:

1. “X is the case at t” is an eternal truth2. X exists eternally

And thus, since eternalism makes this error, is it somewhat a nonsensical position tohold. These two linguistic objections to eternalism, as well as the much larger objectionthat there is no metaphysical presentist/eternalist dichotomy, will be addressed later inthis paper.

3.2 Compatibilist and Incompatibilist Objections

Two other groups of people who reject the RoS argument for BU are the compatibilists andincompatibilists. Compatibilist philosophers of time attempt to hang presentism on a givenrelativistic invariant (like the fact that all inertial frames agree on the ordering of time-likeevents, or “proper time”)12. Incompatibilists, on the other hand, invoke some preferredframe or other entity with which to adorn Minkowski space-time in hopes that this newframe will provide a suitable place to hang presentism and becoming. These positionsconstitute a shift in the definition of “co-reality” as it we presented previously. Bothcompatibilists and incompatibilists would reject our definition and propose another, thoughvarious compatibilists and incompatibilists will propose differing versions of “co-reality”.There are essentially two ways philosophers can and do object to the RoS argument:

12It should be noted that we do not disagree with the compatibilist assertion that to be real somethingmust be “real in all frames”; in fact, we embrace this idea, and it is a central aspect of our definition forreality that frame-invariant properties like time-like separation are necessarily “real” features of space-time.

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1. Reject our characterization of simultaneity in our definition of co-reality (redefinesimultaneity, compatibilist and incompatibilist objection)2. Reject our characterization of reality in our definition of co-reality (reject transitivityof co-reality, compatibilist objection)

Option 1 can and has been justified on several different grounds. It has most famously beenargued that either a) simultaneity is not a suitable criterion for reality because the presentrefers to only the “here and now”, not simply the now, or b) simultaneity is relative to somepreferred foliation of space-time13. Objection a) is raised most famously by Stein[27][28]in his response to Putnam, and objection b) has been raised by various philosophers andphysicists who have rather disparate views as to what the preferred foliation of space-time isand from whence it issues14. We will address both of these objections to the RoS argumentindividually in the following sections.

Compatibilist option 2 is typically raised either by those like Savitt[23] and Dolev[9]who believe that an argument for a transitive reality has not and cannot be convincinglymade especially within the framework of SR or by anti-realists (including solipsists) whobelieve that the phrase “reality” should only pertain to one’s own frame (or, worse yet,only to oneself). The first of these objections is then the only one particularly relevantto the presentist/eternalist debate because an anti-realist would no sooner be a presentistthan an eternalist. The transitivity of “is co-real with” is objected to on this view preciselybecause it leads to the view that presentism is wrong. Thus, it seems like any presentistinterested in saving her stance would object to the transitivity of co-reality implied by ourdefinition of reality as many before her have chosen to do.

4 Response to Objection

4.1 Defining Terms: Establishing a Metaphysical Presentist/EternalistDistinction

Dorato and Savitt claim that there is no metaphysical or empirical distinction betweenthe eternalist and presentist perspectives by critically examining the words “is”, “exists”,and “real” used in several definitions of reality and in doing so point out the shoddy con-clusions that linguistic sloppiness engenders in the presentist/eternalist debate. Our goalin this section is to provide an original definition of reality which supports a metaphysi-cal/empirical distinction between the presentist and eternalist positions. Such a reasonabledefinition is sufficient to counter Dorato’s and Savitt’s deflationary claims15.

13The first of these objections, a), is a compatibilist objection while the second objection, b), is anincompatibilist objection.

14See Cifone (2004, PhilSci Archive) for specific examples of proposed preferred foliations to space-time.15for an alternative response to such a deflation by way of logical and linguistic analysis, see pages 14-17

of Sider[24]

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Our definition of reality relies upon two concepts: “definiteness” and “distinctness”.For an event to be real, we posit, the event must be both definite and distinct. We takea definite event to be one which is meaningfully determined. A useful example of thedistinction between definite and indefinite can be found in quantum mechanics16. Withrespect to a particular variable like spin in the x-direction, a pure-state quantum systemmay be in an eigenstate or a superposition of eigenstates. If there exist a multitudeof systems in the same eigenstate, an x-spin measurement on any of these systems willalways yield the same value. Thus, we say that an eigenstate of x-spin is property-definitewith respect to spin in the x-direction. However, if the system is in a superposition withrespect to x-spin, different systems prepared in the same x-spin superposition may givedifferent x-spin values when measured. There is no way to predict the value of the x-spinof such a superposition after measurement given any information about the system priorto measurement, and as such, the superposition of x-spin is said to be property-indefinitewith respect to x-spin. Generalizing from our characterization of property definiteness, wedefine event-definiteness as definiteness with respect to at least one property. Thus, if anevent is property-definite with respect to at least one property, we say it is event definiteand thus “real”.

We should note here that our event-definiteness criterion is an objective criterion ofa system, and as such, unlike property-definiteness, a system must be indefinite with re-spect to all of its properties to be considered indefinite qua system. Therefore, quantumsuperpositions are not objectively indefinite, for there exists some property with respectto which this superposition is definite by the very nature of superpositions; it is only thex-spin value of such a superposition that is indefinite. If a given event is definite withregard to any property, it is taken to be objectively definite and thus may be real (as longas it meets our distinctness criterion as well, that is).

It should also be pointed out that event-definiteness is a frame-independent propertyof events in the universe; though different observers may disagree about the state of agiven system (as Rovelli[20] points out in his paper on relational quantum mechanics),they will all agree about whether or not it is definite simplicter. One might take issue withour assertion of the frame-independence of definiteness; for instance, some postulate thatquantum collapse is hyperplane-dependent, and thus an observer in one frame will see aquantum system as having some definite property “y” while an observer in another framemight observe y to be indefinite. However, even if collapse is so dependent, the fact remainsthat each of these observers will observe there to be some definite property “z”, and thus,by our definition, one must take the quantum superposition to be definite qua system.

16We are not claiming that quantum superpositions are unreal or non-existent simplicter; rather, we areproviding an example in an instrumental spirit of how a property might be indefinite and thus suggesting howone might generalize from this example to form an idea of general indefiniteness. This indefiniteness, if madegeneral and applicable to all properties, would make an event effectively unreal. However, superpositionsthemselves are by their very nature in a determinate state with regard to some property, so they areobviously not wholly unreal.

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That is, there is no frame of reference from which one can observe the quantum systemin question to be without any definite properties. Therefore, our definition of definitenessdirectly implies the kind of transitivity we exploit in our RoS argument17.

The other criterion for an event to be real is that it must be distinct. A distinctevent must be in some way different from other distinct events (a la Leibniz, call it thediscernability of non-identicals). Such a criterion for the distinctness of events is differentfrom a criterion that requires the distinctness of particles. While it may be that twocompletely indistinguishable particles can both be distinct, the issue of concern here is thereality of events, and it is the case that two completely indistinguishable events cannot bedistinct per the identity of indiscernables; or if you prefer, two completely indistinguishableevents cannot be numerically distinct. This criterion of distinctness may be viewed as amore pragmatic concern (we have no reason to take event B to be numerically distinctfrom event A if all of B’s properties are identical to A’s). Such a criterion of reality keepsone from treating as real two (allegedly distinct) “events” that might seem to be differentbut are truly one and the same event — the differences are purely perspectival as in theLorentz transformations of SR. For example, as per Newton’s third law of motion, there isno need for us to count as distinct both the event of a car hitting a wall and the event ofthe wall hitting the car; they are simply two different ways of viewing the same singularevent18.

Having established these two criteria for reality, does there appear to be a differencebetween the presentist and eternalist positions? The answer is “yes” because the distinct-ness and definiteness of the past and future are not analytic. The presentist claims thatpast and future events lack both/either definiteness and distinctness simpliciter while theeternalist says all events past, present and future possess both definiteness and distinct-ness simpliciter. The first fact to note about the future is that it is unknown to us. Onemight even be tempted to say that it appears indefinite since it seems (at least on somestochastic accounts of quantum outcomes) that there is no way for us to know the future(in principle) no matter how much we know about the present. Such stochastic accountsof objective quantum indefiniteness (as opposed to subjective quantum indefiniteness for

17We should point out here that presentists who claim that there simply are no past or future events canbe treated as taking such event as indefinite on our picture here, since a non-existent event cannot haveany definite properties. Thus, our account of definiteness provides a criterion for reality that explains thispossible presentist stance.

18One might well wonder what purpose introducing “distinctness” as a criterion here serves above andbeyond the work already done by definiteness. Distinctness is important in this discussion because it allowsfor nuances within possible presentist positions. We believe there may be presentists who concede thatsome future events are determined in that they have some definite property, yet who may still reject thatthe future and present are “equally real”. They could do so by way of distinctness, claiming that thereare an infinite number of events (one of which will be actual, the rest of which will not be) which are all“definite” in some sense but are indistinguishable. The future would thus be definite but not distinct, andso the presentist could write it off as unreal. For the purposes of this discussion, it is in our interests togive as many reasonable possibilities to the presentist as we can, and so we have included distinctness inour discussion.

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deterministic interpretations) should not be confused with what we will call O- (objective)indefiniteness and S- (subjective) indefiniteness more generally. O- and S-indefiniteness arebest understood as a different kind of indefiniteness entirely which will be made clearer byan appeal to the idea of “Newton’s god” (NG), an entity in the 5th or higher dimension“looking down” at her space-time “sensorium”.

Depending on whether the future is O-indefinite or S-indefinite, NG would observedifferent things as she looked down on her “sensorium”. If the future and past are S-indefinite only, NG would physically see19 the past, present, and future — all of space-time,a 4D BU. NG would see events in the past, present, and future — a static multi-coloredmarble of world-lines/tubes, if you will. If the future and past are truly O-indefinite,however, NG would not be able to see the future or past from her 5th-dimensional perch,but only a continually temporally evolving present. If the future is truly O-indefinite, itdoes not matter whether NG is observing us flipping a coin or measuring the spin of anelectron with stochastic outcomes; either way, she will not observe the future outcome, andlikewise if the future is merely S-indefinite then in both the classical and quantum case NGwill observe the future outcome. In the O-indefinite case, NG may be able to predict theoutcome just as any one of us may be able to predict the outcome of a coin flip, but NGwill not be able to observe this future outcome.

The eternalist, presentist, and possibilist positions become clear and distinct given thischaracterization of O- and S-indefiniteness. Eternalists believe that the future and past areonly S-indefinite; though beings within space-time may not be able to observe the past orthe future, a being outside of space-time would be able to easily observe them. Thus, NGsees a 4D BU when she looks “down on” the universe. The presentist, on the other hand,holds both the past and future as truly O-indefinite and thus believes that NG would seean evolving 3D time-slice of the universe when she looks “down on” her “sensorium”20.Finally, the possibilist takes the future to be O-indefinite but the past S-indefinite only,thus leading to the belief that NG would see a growing BU when she looks “down” on theuniverse. Diagrams of these various NG perspectives may be found in Appendix C.

Another way of viewing our “Newton’s god” argument is in terms of “where” time is inthe presentist picture compared to the eternalist picture. In the presentist picture, NG isstill constrained by time. The fact that NG is removed from the strictures of the universedoes not entail her separation from some notion of time in which she must still continue toexist. It is possible, then, for NG to remove herself from space without removing herselffrom time on the presentist picture. On the eternalist picture, however, NG is free from thestrictures of temporality. It is unclear what the character of the 5D universe NG inhabits is(the 5th dimension could be conceived as some sort of second-order time, a 4th-order space,or some phenomenology of dimensions we do not experience); however, the point is that

19When discussing what NG “sees” we are only invoking the traditional physical sensory modalities ofthis entity. We make no claims about other ways of knowing or omniscience that one in NG’s positionmight be able to employ by means other than perception.

20On some presentist views, she might even see a point. See Stein (1968) for more on this.

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NG is free from time as well as space as it exists in the BU since the two are inextricablylinked, and thus time has the same ontological status as space. The eternalist does nothave to argue that time behaves the same way as space does, simply that time and spaceare inextricably linked, which is a stance that the presentist rejects.

There may be some who believe that NG is not a suitable tool for dealing with thepresentist/eternalist distinction; in particular, one might find our NG question-beggingsince a god’s eye point of view might somehow allegedly violate basic tenets of SR; however,one must note that by hypothesis NG is removed from the 4D-manifold (space-time) thatshe observes. Such a being would be constrained to see a space-time that conforms tospecial relativity even though this “god-frame” itself would not so conform. SR can onlymake claims about perceptions of space-time from within space-time, and since this “god-frame” is outside of space-time, this relativistic objection does not obtain. Even withoutpositing the existence of NG or even a position from which NG could look, we have alreadyshown that the presentist/eternalist distinction can be stated in terms of the separability ofspace and time, and so if this objection to NG as question-begging is simply that one cannotremove oneself from space without removing oneself from time as well, then the objectionhas already conceded our point to us. Using our novel argument for the eternalist position,Dorato’s two previous objections to eternalism can be ignored as well. Nowhere in ourargument do we claim that the past, present, and future are all “simultaneous”, nor isthere any confusion between eternal truths about existence and the eternal persistence ofevents. First, an appeal to some sort of “second order” time is completely unnecessary forour formulation of the eternalist position, and as such the accompanying language of the“past present, and future existing simultaneously” has been discarded. As noted above,Newton’s god’s frame need not necessarily be conceived as some sort of second order time;further, it is merely a thought experiment to show that Dorato/Savitt type arguments aredependent on verificationism of a sort special relativity need not entail. In the followingpassage Dainton[8] paints a suggestive picture of what it means to take Newton’s god’sperspective of the BU seriously:

Imagine that I am a God-like being who has decided to design and then create a logicallyconsistent universe with laws of nature similar to those that obtain in our universeSincethe universe will be of the block-variety I will have to create it as a whole: the beginning,middle and end will come into being togetherWell, assume that our universe is a staticblock, even if it never ’came into being’, it nonetheless exists (timelessly) as a coherentwhole, containing a globally consistent spread of events. At the weakest level,“consistency” here simply means that the laws of logic are obeyed, but in the case ofuniverses like our own, where there are universe-wide laws of nature, the consistencyconstraint is stronger: everything that happens is in accord with the laws of nature. Insaying that the consistency is “global” I mean that the different parts of the universeall have to fit smoothly together, rather like the pieces of a well-made mosaic or jigsawpuzzle.

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It would be absurd to argue, therefore, that two perspectives as different as these are, arein fact, metaphysically and empirically equivalent in principle; such a claim could onlybe sensible if one assumes a spatiotemporal-anthropocentric verificationism and there isno non-question begging reason to do so. For this reason, Dorato’s and Savitt’s granderclaims must be dismissed. The most these two authors can suggest is that a better definitionof reality is necessary before the presentist/eternalist debate can be undertaken, and so,with such a definition provided, Dorato’s and Savitt’s deflationary claims can be ignored.Dorato and Savitt are right to point out concerns with definitions of terms (such as “real”)in arguments such as ours, but generally speaking this is the most that linguistic analysiscan contribute to the presentism/eternalism debate. The most such appeals can do isdetermine that certain positions in the debate are “unspeakables” or that the languageused must be clarified for the debate to proceed.

4.2 The Transitivity of Reality

Our new definition of an event’s reality as a combination of definiteness and distinctnessalso has implications for the second compatibilist objection to the RoS argument, namelythat there is no good reason why reality or the “is co-real with” relation ought to betransitive. The first response to this claim is that any relativistically invariant relationalproperty must be transitive across all reference frames. For example, consider the propertyof “light-likeness along direction x ”21. Any two events that are light-like separated in somedirection share this property, and all observers in all frames will agree that two events arelight-like separated if they are so due to the fact that the speed of light in a vacuum isa universal constant. Thus, if event A is light-like separated from event B and event Bis light-like separated from event C in the same direction, then event A must be light-like separated from event C (in this same direction). This deduction is true even if oneadds different relativistic frames into the equation. For instance, if event A is light-likeseparated from event B in direction x in a frame moving with velocity v and event B islight-like separated from event C in direction x in a frame moving with velocity u where u isnot equal to v, it is still the case that event A and event C are light-like separated in a framemoving with velocity w no matter what the value of w22. Thus, from this simple example,one can see that a relativistic invariant quantity is transitive across inertial frames.

There are two other relativistic invariant properties aside from “light-likeness” that wewould like to discuss now. The first of these is number. All observers, no matter theirframe, will agree on the number of events that occur. Thus, no matter what frame an

21The “x” in “along direction x” in this property should be a four-dimensional vector pointing from oneevent to the other. We include this condition to rule out the following, non-transitive case: consider a lightbeam shot out from a spaceship at A, reflected off of a mirror at B, and returned to the ship at C. A and Bare light-like, B and C are light-like, but A and C are time-like. However, this non-transitivity arises fromthe fact that the direction of the light is changed at B, and so the vector x shifts at this point. We thankGordon Belot for bringing this objection to our attention.

22Within relativistic limits, of course.

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observer is in, it will never be the case that she will see an event take place that anotherobserver does or could not see. Though observers may disagree about some of the propertiesof an event, no observer will see a “novel” event; that is, there is no event simpliciter thatone can only see if one is in a certain reference frame. This means that the very existence,the very definiteness of an event-as-such must be a relativistic invariant, and thus as perour pre-established criterion, definiteness must be transitive across frames.

Another relativistic invariant is the space-time interval between two events. This sep-aration is defined by the space-time metric as: s2 = t2 − x2 − y2 − z2 where “s” is thespace-time interval, “t” represents time, and “x”, “y”, and “z” are spatial coordinates in3-space. Because the interval between events is an invariant, it is always possible for ob-servers in different frames to distinguish between different space-time events in a consistentmanner. Because of this, no observer will confuse two events that are seen as distinct inanother frame. Thus, the invariance of the space-time interval implies that distinctness isa relativistic invariant. Thus, as per our pre-established criterion, distinctness also mustbe transitive across frames.

Now, since reality in our formulation has definiteness and distinctness as necessary andsufficient conditions and since both definiteness and distinctness are relativistic invariants,it follows that reality, the conjunction of definiteness and distinctness, should also be a rel-ativistic invariant. Finally, as has already been established, any relativistic invariant mustbe transitive across frames, and therefore our “equal reality” relation must be transitiveacross frames. This argument suggests that, as a logical consequence of special relativ-ity combined with our definition for reality, the frame-independent reality of the universemust obtain. This logic provides more than sufficient reasoning to support objectivity inour co-reality definition, and so the weight now falls on the shoulders of Savitt and thepresentists to explain why “is real for” should not be transitive if they want to continuepushing this point.

4.3 Against the Point Presentist

There have been several arguments against the “here, now” presentist as Stein23 presentshim. This variety of presentist holds the present to consist of a single point in space-timeand defines the “now” as both temporal and spatial. There have already been severalexcellent responses to Stein’s view, most notably those provided by Cifone (2004) andPetkov[16]. We will here reiterate and rephrase Cifone’s and Petkov’s points to show thatthe “point” presentists, as they are traditionally called, do not hold a viable position.

The first argument against point presentism comes from Cifone. As previously dis-23Bourne (2007) points out that Stein was not assuming a “common sense” notion of simultaneity when

he attempted to redefine simultaneity within relativity as the “here” and the “now”. It seems that Stein’soriginal point was not so much that simultaneity had a different nature than previously thought but ratherthat the conception of simultaneity that comes to play in everyday discourse has no currency in specialrelativity.

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cussed, it is easy enough to see how anti-realism can be reduced to a form of point presen-tism, but the opposite seems true as well. Point presentists can be taken to be essentiallysolipsists since what exists at only one point (presumably, the point where the point pre-sentist currently exists) is all that exists. This is not an argument in itself, and there areways around point presentist solipsism, but these views are almost equally bad. If thereis more than one “point present” in the world (that is, if he rejects solipsism), what isrequired for a point to be “the present”? Is there some “present-maker” that defines thepresent, that selects it out from all possible “presents”? And if there is, what would sucha “present-maker” be? What is more, if there are a large number of “presents” that allcompose reality, why do none of them agree with each other? For if the present is only asingle point, it follows that multiple “nows” will not count other “nows” as real. There willbe no agreement among different observers in different frames, let alone different observersin the same frame, as to what constitutes reality. Thus, it seems that the point presentistloses all semblance of self-consistency when he explains his position and runs the risk ofhaving his position collapsed into absurdity.

Perhaps most damning to the point presentist, however, is Petkov’s response. Petkovpoints out that a point presentist reduces reality to a single, 0-dimensional point. If pointpresentism is the case, he asks, why does the universe appear to be four-dimensional, asevidenced by the aforementioned 4D space-time invariants? The universe defended bypresentism which lacks the 4D-manifold in favor of a 3D universe seems unable to supportor explain phenomena like length contraction and time dilation, but it appears nearlyimpossible to reconcile a 0-dimensional view of space-time with such phenomena. Such aview, Petkov argues, reduces to solipsism. After all, consider two observers A and B. IfA and B are distinct observers, any observation event by observer A will not be real toobserver B since only observer B’s “here and now” are real to him. This solipsism leadsto the loss of realism that Cifone (2004) points out. Petkov also claims that only a 4Dview is supported by special relativity by refuting the 3D picture of the world as well. Hisargument is that the phenomena of length contraction and time dilation, both of whichallow different observers to hold ontologically distinct and correct beliefs about the 3Dproperties of an object, cannot be as completely described by a 3D worldview as by a 4Dblock universe view. He compares the situation to looking at a 2D plane; one can certainlydescribe the plane as a series of lines in the x-direction for different, constant values in they-direction, but this “complete” description of the phenomenon does not change the factthat it is a 2D plane and not a 1D line that is being described. If a 3D world is inadequate,then, it stands to reason that lower dimensional representations of spacetime would likewisebe inadequate. Thus, the 0D description of the world presented by the point presentistmust be incorrect. If one is to believe in the point presentist as a viable alternative to theeternalist and the traditional presentist, the point presentist must provide physical supportfor a 0D universe or else abandon his view.

Before leaving point presentism, however, there is one perspective similar to Stein’sthat advocates changing the definition of simultaneity in order to save the presentist from

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the RoS argument. This more recent shift is presented by Bourne[2] and ought to be ad-dressed here since it is a challenge to the notion of simultaneity we employ, a challenge thatadheres to the logic that Stein originally used when proposing point presentism (see previ-ous footnote). Bourne argues that simultaneity is absolute within space-time. Accordingto Bourne, the notion of absolute reality does not translate into the language of relativitybecause no one can determine whether or not two events are simultaneous by observationswithin a frame. He turns simultaneity on its head in presentism, not by defining “whatis real” by “what is present” but rather “what is present” by “what is real.” Bourne ap-peals to a linguistic analysis in terms of conjunction, instead of observables in the worldas the basis for reality and thus simultaneity. In short, Bourne’s reinterpretation of simul-taneity insists that simultaneity is absolute by ruling out the possibility of determiningsimultaneous events (or, it seems, reality) by observation alone.

Bourne’s reinterpretation of simultaneity shows to what extremes presentists must goto rescue their philosophy of time from the RoS argument. By the time Bourne is finishedwith simultaneity, there is nothing resembling the common-sense notion of simultaneity left.Not only is simultaneity dictated as absolute without empirical evidence or verification (forsurely one cannot appeal to physical grounds for such an argument), but simultaneity hasnow also been removed from the realm of science altogether. There is no longer any ob-servation that can determine if two things occur at the same time! Not only does thisassertion fly in the face of common-sense views of simultaneity, it also poses dire conse-quences for science and human knowledge when combined with presentism. If Bourne’ssimultaneity gives us no access to a distinctively “real” character for “real” events, howcan any empirical evidence help in determining which things are real and which things arenot? Does linguistics then pose a better means to come to truths about the natural worldthan science does for Bourne? If we are planning on choosing a metaphysics of time thatbest accounts for the phenomena at hand without making any wild metaphysical claims, itseems clear that Bourne’s reinterpretation of simultaneity does not save presentism sinceeven the claim that the past, present, and future are all equally real is a more conservativeclaim than that simultaneity and reality are both phenomena to which no one has empiricalaccess.

It is, however, possible that one can reinterpret Bourne’s claims about the simultaneityin physical terms; such a reinterpretation of Bourne’s simultaneity would necessitate apreferred foliation of space-time24. Though we will not address Bourne’s revised notionof simultaneity directly any further since he does not explain his simultaneity in terms ofpreferred foliations of space-time in any satisfying way, we will address preferred foliationpresentists generally in the next section.

24Bourne explicitly endorses such preferred-foliation presentists in his book, though he does so in adifferent section from the one in which he advocates his radical revision of simultaneity.

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4.4 Preferred Foliations in Space-Time

A slightly tougher objection to RoS is raised by those suggesting that space-time has apreferred foliation. Such a foliation would run counter to current beliefs not only abouteternalism but about relativity as well, for one of the chief tenets of relativity as it istraditionally interpreted25 is that there exists no preferred reference frame. The good newsfor the eternalist is that there is very little physical evidence26 to support such a preferredfoliation, but it such preferred foliations may be postulated. Assuming that such a foliationis found, then, does our RoS argument for BU still follow?

The first response to the preferred foliation objection is that no preferred foliation the-ory as it currently stands, even if it were proven to be true, provides the necessary physicalmechanisms that would be necessary to explain why such a frame would be preferred.Until physical motivation for a preferred frame is provided, one cannot abandon the RoSargument. Perhaps there is some way in which the “now” transforms as it goes into otherframes. Perhaps the “now”, though it is dependent on its preferred space-time foliation, isstill present or still has metaphysical influence on other frames. Until physical motivationfor a preferred reference frame is provided, one simply cannot know these things. Afterall, we do use CMBR (“cosmic time”) as a pragmatic preferred frame in physics but itdoes not impugn BU any more than proper time does. In a purely relativistic contextthe claim that the Big bang occurred 14 billion years ago is completely frame dependent,there are other possible, equally valid choices to be made. The point is that none of theseinvariant features internal to SR changes the fact that M4 unadorned has no resources toconstruct an absolute and objective preferred frame and that RoS implies the reality of allevents. On our view, one can always conventionally define a preferred frame such as cosmictime; however, unless one can show that a preferred frame a la a physical mechanism isthe cause of physical effects like Lorentz contraction and time dilation (as opposed to mererelativistic effects), a pragmatic-preferred frame of this sort does not negate BU27.

25Other non-standard interpretations, like the Lorentz interpretation, yield the same results as the M4,no preferred frame interpretation of space-time, so it should be pointed out that it is not the physical resultsof special relativity that are threatened by the preferred frame but rather the currently-held understandingof special relativity which is under fire. See Appendix A for more information on the rejection of thegeometrical special relativity interpretation.

26There are those who claim that at the end of the day, a correct theory of quantum gravity or a correctinterpretation of quantum mechanics (such as Bohmian mechanics) might yield an absolute preferred frame.While technically true, recent work by Callender[5] and Monton[15] suggests that: a) an absolute preferredframe is not a likely consequence of future theorizing in either case and b) even if these preferred-foliationtheories do pan out as expected, they will run into all the problems outlined in this section.

27Another objection to such a move comes from John Mather, winner of the 2006 Nobel prize in physicswith George Smoot for their discovery of the blackbody form and anisotropy of the cosmic microwavebackground radiation, in a talk given at Swarthmore College in October 2007. In his talk, Mather suggestedthat there may be many “preferred frames” provided by the CMBR depending on how the source of theCMBR is moving. If there are, in fact, a multitude of “preferred frames”, any idea of “reality” that couldbe grounded in CMBR would be useless for presentism because our uniqueness criterion would be violated.There would be many “real” frames that one could choose. It should also be noted that Mather himself

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Callender’s[5] objection to the preferred foliation view, however, is perhaps stronger.Callender proposes a problem he calls the “coordination problem”. The idea is that evenif there is a preferred reference frame28, there is no reason to believe that this referenceframe would provide anyone with a suitable “now” upon which to base presentism. Onemust in some way prove that the physical preferred frame is precisely the same as themetaphysical preferred frame posited by the presentists. How would one be able to makesuch an association? And, perhaps more importantly, even if it were possible for one toargue that the physical and metaphysical preferred frames were, in fact, one in the same,how would this alter the presentist’s conception of the present?

Let us try to cash out what it would mean to live in a universe in which a preferred frameforms the basis for an absolute reality. Imagine two twins who are born in such a preferredfoliation of space-time. The absolute simultaneity of the preferred frame mandates thatthese two twins will agree on their ages at all points in time (twin 1, Alice, will turn21 when twin 2, Bob, turns 21, etc.). However, if Bob decides to take a trip and leavethe “real” foliation of space-time, the “absolutely simultaneous” events (picked out basedon the preferred frame) involving Alice and Bob describe Alice and Bob as being differentages (Alice, perhaps, is 23 while Bob is only 22); however, whenever Alice and Bob interactdirectly with each other by shaking hands, giving each other a high five, etc., they will agreethat they are both the same age. According to the preferred frame presentist, then, Bob’sleaving Alice’s frame changes his ontological status. His age and size physically change ashe travels around the universe, yet Bob is completely unaware that he is undergoing thesechanges.

This situation produces several problems for the presentist since she must explain whychanging one’s velocity should cause one’s views about oneself to be more or less in linewith “reality.” When I get in my car and drive to the store, for instance, I have changed myinertial frame; am I now closer to the “real” frame or farther from it? Either way, I don’texperience the immediate world differently, nor do I perceive any differences in myself, yetmy ontological status has changed. What, then, is the basis for calling such a velocity shifta “shift into (or out of) delusion” since I notice no difference in myself when I speed upor slow down? The other problem for the preferred frame presentist is a related concern:if the preferred frame is what’s “real” but I experience the world in exactly the same waywhether I’m in the preferred frame or not, why should I care about “reality”? What makesreality a meaningful concept to me if it is not linked with any physical, psychological,or epistemological change? For a preferred frame presentist, reality has no importantimplications other than to save presentism. Again, reality becomes distantly removed from

does not believe that the CMBR frame should be treated as anything more than a useful frame for doingcalculations; that is, like the proper time frame, the CMBR frame is not “real” in some special way but israther just a helpful tool for physical calculations (Mather 2007, personal communication)

28Specifically, Callender is concerned with a preferred reference frame that might emerge from robustviolations of the locality principle in Bohmian mechanics (and other modal interpretations) or preferredframes required for instantaneous collapse in some collapse accounts of quantum mechanics.

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our experiences, and though we may be able to convert all of our dimensions, temporal andspatial, into our “real” dimensions according to the preferred frame, these real dimensionswill be no more important to our lives than our dimensions according to any other frame.

In the end it seems like the preferred foliation proponent is providing a view that isperhaps as inimical to the presentist as to the eternalist. One of the major reasons why pre-sentists hold the position they do is that it seems to agree with human manifest experienceof time. If this experience were hung on some preferred frame due to microwave backgroundradiation or preferred frames as posited by some Bohmians and collapse theorists, it wouldbe possible for a “now” to exist that was completely alien to human experience. Does thephrase “now” even have any meaning when it has been removed from human perceptionsof time? The burden falls to the presentists here to prove that a meaningful “now”, aphysical preferred foliation of space-time, and an identical metaphysical preferred foliationof space-time are all compatible, and since no such reconciliation of all three of these ideashas been provided by the presentist camp, we are forced to conclude with Saunders[21] thatthe burden of proof in the presentism/eternalism debate lies entirely on the shoulders ofpresentists instead of with the eternalists because there is nothing obvious in the resourcesof M4 alone to be a preferred frame to ground presentism, at least nothing not ad hoc,merely pragmatic, or perspectival.

4.5 The Spatial Presentist: Absurdity in Incompatibilist Presentism?

Having answered the presentist objections of the RoS argument in turn, we would like topropose another argument along the same lines as the RoS argument which, we believe,should serve as a preemptive criticism against incompatibilist presentist arguments to come.Suppose that there exists a new kind of realist called a spatial presentist. The spatialpresentist believes not that all events occurring simultaneously are real but that all eventsthat occur in the same place are real. Perhaps there is a sphere (infinitesimally small, forour purposes) that the spatial presentist has set aside, following which he claims that “theonly things that are real are those in this sphere”. One might ask, then, what would bereal after the creation of the sphere at an event A in the above diagram, which shows, fromrelativistic considerations, what will be real.

From Figure 2, it is clear that we are left in a situation directly analogous to thetemporal presentist situation previously established in our RoS argument, for the abovespace-time diagram shows a property we will call the relativity of same position or RoSP.One can simply rotate our Figure 1 and make a RoSP argument to disprove spatial pre-sentism in the same way that the RoS argument disproves temporal presentism. Thearguments are completely symmetrical in the same way that RoSP is symmetrical withRoS.

But what does this show? Only that if an incompatibilist presentist of the non-spatialvariety wants to assert that temporal presentism and temporal presentism alone is correctby proposing some new feature of space-time, she must be careful that her argument and

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Figure 2: Spatial Presentist Argument

mechanism establish presentism but do not allow for spatial presentism29. This is yetanother burden that the incompatibilist presentist must carry. The symmetry betweenRoS and RoSP suggests that incompatibilist presentists must establish a physical basis fortemporal asymmetry so that spatial presentism does not become as viable and defensiblea position as presentism itself, for reconciliation between spatial and temporal presentismmust lead to point presentism, which we previously discussed.

5 Conclusion

Though the traditional formulations of the Putnam, Rietdijk and SSC’s RoS argumentfor the block universe may be ill-defined in certain parts that leave the argument open toattacks by philosophers of language and presentists, we have reformulated the argumentwith more specific definitions that make eternalism the likely victor over presentism. Thus,the task before the presentist in defending herself has become even grander; she must1) find a way to dispel the RoS argument, 2) show why presentism is more likely thaneternalism, and 3) integrate temporal asymmetry as fundamental to her argument lest herargument run the risk of establishing an obviously false view (spatial presentism) as well asit establishes her temporal presentism30. It is clear from the forgoing that the most commonpresentist argument that “space and time are not perceived to act in the same way” is notsufficient to shoulder the weight of a full presentist defense, and thus a more developed

29This is, of course, assuming that the presentist in question is not a point presentist or some new formof presentist who wishes to tie the conception of the “now” together with some more evolved conception ofthe “here.”

30We would like to note at this point that there is an obvious reason why spatial presentism has nevercaught on in the philosophy of time: it does not agree with our perceptions of reality. However, if one wantsto dismiss spatial presentism on these grounds but remain a presentist, one’s workload is not lessened sinceone must now conclusively prove a link between experiences and reality.

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presentist argument addressing all of our concerns must be proposed before presentism canescape from the jaws of the RoS argument. Even the retreat into the position of Savitt andDorato that there is no significant difference between presentism and eternalism seems adifficult one to hold in light of definitions for definiteness and distinctness like the ones wehave provided. And so, in conclusion, we echo Saunders in stating that while eternalism initself may not have been deductively established by our arguments, the burden falls uponthe presentist to show why eternalism is not much more probable31.

6 Appendix A: Against the Dynamical interpretation of Spe-cial Relativity

Various people have defended a dynamical interpretation (“constructive” in Einstein’s lan-guage) of SR of late (e.g. Brown, 2005). In the following passage Callender[5] claims thelatter interpretation is a potential problem for the RoS argument for BU:

In my opinion, by far the best way for the tenser to respond to Putnam et al. is toadopt the Lorentz 1915 interpretation of time dilation and Fitzgerald contraction.Lorentz attributed these effects (and hence the famous null results regarding anaether) to the Lorentz invariance of the dynamical laws governing matter and radiation,not to spacetime structure. On this view, Lorentz invariance is not a spacetimesymmetry but a dynamical symmetry, and the special relativistic effects of dilation andcontraction are not purely kinematical. The background spacetime is Newtonian orneo-Newtonian, not Minkowskian. Both Newtonian and neo-Newtonian spacetimeinclude a global absolute simultaneity among their invariant structures (with Newtonianspacetime singling out one of neo-Newtonian spacetime’s many preferred inertial framesas the rest frame). On this picture, there is no relativity of simultaneity and spacetimeis uniquely decomposable into space and time. Nonetheless, because matter andradiation transform between different frames via the Lorentz transformations, thetheory is empirically adequate. Putnam’s argument has no purchase here becauseLorentz invariance has no repercussions for the structure of space and time. Moreover,the theory shouldn’t be viewed as a desperate attempt to save absolute simultaneity inthe face of the phenomena, but it should rather be viewed as a natural extension of thewell-known Lorentz invariance of the free Maxwell equations. The reason why sometensers have sought all manner of strange replacements for special relativity whenthis comparatively elegant theory exists is baffling (2006, 3).

31We would like to thank Mark Stuckey, Michael Cifone, David Baker, Gordon Belot, and the audienceat the 3rd International Ontology of Spacetime Conference at Concordia University in 2008 for commentson previous versions of this paper.

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See also Harvey Brown’s book Physical Relativity[3] and his essay “Minkowski Space-time:A Glorious Non-Entity”[4] co-authored with Oliver Pooley for a more developed argumentfor this stance.

First, Brown (2005, p. vii) himself is clear that he is not defending either ether or apreferred-frame, unlike Lorentz himself. We grant that SR is neutral about the ontologyof spacetime, but we think there are good reasons for preferring the kinematical over thedynamical interpretation, though we cannot pursue them here32. We do want to notethat we are not convinced of Callenders claim that the dynamical interpretation of SRnecessarily negates the RoS. At least in the case of Brown, who again, does not claim to bedefending absolute simultaneity, while his arguments may lead to spacetime relationalism,they do not obviously entail the falsity of RoS as such. So until someone provides a cogentargument from spacetime relationalism to the falsity of the RoS, our argument remains intact.

Second, even granting an absolute frame, Browns dynamical interpretation does notobviously save the presentist since she must still face some of the problems raised in Section4.4. For example, even if there is an absolute space-time and a universal moment of thepresent, there is no reason to believe, as per Callenders objection discussed in Section 4.4,that such a present lines up with human experience of the present. What is more, as longas Lorentz contractions and dilations exist, one observer traveling at relativistic velocitiesmay observe his present to be different from the present of those around him. Does thatmean that, since he is dealing with past or future versions of these other beings, that theyare not real since they are not actually experiencing the present simultaneously with therelativistic observer? There seems to be a suggestion of some sort of frame-dependentsolipsism, which would constitute an anti-realism that presentists would reject as readilyas eternalists.

Finally, if we are to take seriously the implication that quantum mechanics (our besttheory of matter) is to special relativity what statistical mechanics is to thermodynamics,then had not quantum mechanics better be able to explain (in some robust sense of theword) the key features of SR such as Lorentz invariance? Obviously, this condition has notbeen met and merely interpreting Lorentz invariance to be restricted to dynamical lawsonly hardly does the trick.

7 Appendix B: Objection to RoS Argument by Meta-Time

One of the points we believe we have established in this paper is that the eternalist per-spective does not require any meta-time or generally any 5th dimension to be coherent;

32See Michel Janssens Drawing the line between kinematics and dynamics in special relativity in the Phil.Sci. archive (reference number 3895) for good arguments favoring the kinematical interpretation. See alsoPetkov (2007) where the kinematic interpretation of Minkowski space-time realism has consequences noteasily or obviously accounted for by the dynamical interpretation.

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however, one might object that our R-value, R-relation language itself begs the questionagainst eternalism and refutes our repeated assertion that no eternalist meta-time is nec-essary. The objection might go as follows: Suppose that one is committed to simply abinary ontology of R-values such that an R-value of 1 represents “real” and an R-value of0 represents “unreal”. The eternalist perspective here seems straightforward (all R-valuesare 1), but the presentist perspective is not so straightforward. At time t1, only eventsat time t1 have an R-value of 1 while all other space-time events have an R-value of 0.At time t0, only events at t0 have an R-value of 1 while all other space-time events havean R-value of 0. Thus, if t1 is not the same as t0 (that is, as long as space-time has atemporal dimension), R-values must change with time, meaning that there must be somesort of extra dimension posited to account for this notion of change. Thus, one mightobject that the only way for one to meaningfully capture the presentist perspective usingR-values is to assume some sort of meta-time, and thus the eternalist is only right if oneassumes meta-time, which is to give the eternalist his conclusion from the start. Thus, theRoS argument seems to both beg the question and assume meta-time.

Our response to this objection is to note that the objector has taken a fairly narrowlyview of R-values (though, to be fair, this nave view is essentially the one we advocate inthis paper for the sake of simplicity). There is no reason why R-values cannot be tweakedto suit the presentists’ notion of reality. Let us allow a different kind of R-value, then, onemore in keeping with predicates such as Goodman’s infamous “grue”. We now define aseries of R-values that can take any value we would ascribe to time from the beginning oftime to the end of time. Each R-value represents the predicate “is real at time x and isunreal elsewhere” where “x” is the R-value of the event. Such an R-value scheme is static;there is no meta-time required to account for changes in R-values because no matter whattime we perceive it to be, the R-value of every event will remain the same. Thus, by re-characterizing R-values in terms of the time of various events, we can avoid this objectionto the RoS argument33.

Still, there remains a further issue: time alone is not enough to provide us with properR-values, especially not in the relativistic context we assume for the RoS argument to gothrough. Since time is a frame-dependent quantity, it seems that, by allowing grue-like R-values that are based on temporal coordinates, we are forced to give up on the objectivityand frame-independence of R-values. What this shows, however, is not that R-values arenot objective but that time itself is not the proper quantity to base an R-value on. Instead,the R-value used for the presentist ought to be the proper time or the space-time interval

33One might wonder about how we would treat the perspectives of presentists who expect the present tohave a certain duration instead of being instantaneous. The answer would be to transform the R-value intoan R-vector, with the first entry representing the time at which the event switches from “unreal” to “real”and the second entry representing the time at which the event switches from “real” to “unreal” again.This vector scheme could account for event absurdly complex presentist/possibilist/historicist positionsthat have events blinking into and out of existence many, many times by simply characterizing each shiftfrom real to unreal (and back again) in terms of the time at which the shift occurs and characterizing theR-vector of the event in terms of these times.

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from some fixed point. Such quantities retain the essential character of our R-value time-dependence while still providing the objectivity we seek from an R-value. Thus, if thepresentists’ R-values are defined as the proper time at which a given event is real, then theR-value has the character we expect and the RoS argument goes through without beggingthe question or assuming meta-time.

One final remark ought to be made, however: why should we not stop by just definingthe presentists’ R-values in terms of time instead of proper time? We lose objectivity indoing so but seem to better capture our intuitions about time and the present. The answer,we believe, comes back to what the R-values are to represent: reality and ontologicalstatus. It seems that, if anything ought to be frame-independent, it ought to be theontological status of an event. If events are capable of having some frame-independentproperties, such as proper time, distance via the space-time interval, and the kind of event-definiteness and distinctness we previously discussed, then it would seem ridiculous to saythat the fundamental ontological status of the event, which ought to be its most crucial,fundamental, essential property, is somehow less objective than these frame-independentproperties. This disagreement may boil down to which intuitions are most important tocapture: intuitions about reality, or intuitions about the behavior of time. Given the factthat human intuitions concerning time seem at best incomplete and at worst wrong in manycases, we believe that it is reasonable to prefer capturing the former intuition to capturingthe latter. As such, we believe that defining presentist R-values in terms of proper time, aswe suggest in this section, is the best way to nuance R-values so as to reconcile them withpresentism: not only does it allow the RoS argument to follow as we’ve characterized it,it also reconciles our intuitions about reality with presentism in the most reasonable waypossible.

8 Appendix C: A “God’s Eye” View of Space-Time on Dif-ferent Theories of Time

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Figure 3: Eternalist Perspective on Space-time

Figure 4: Presentist Perspective on Space-time

Figure 5: Possibilist Perspective on Space-time

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Figure 6: Point Presentist Perspective on Space-time. This perspective, idealized here as asingle point in space-time, is the most difficult to represent visually since it should have aninfinitesimal size. The single dot of the present is the only thing in space-time that existson this view of space-time, making it a much more limited and precise view of the presentthan the more general form of presentism previously represented.

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